Computational Study of the Structures of Gaseous Helium-3 at Low Temperature

Abstract

A computational study of gaseous helium-3 at T=5.23 K, for number densities rho N<0.0021 A(-3), analyzing the different pair and triplet structures in both the r and the k spaces, is presented. Structures in r space (i.e., instantaneous, total continuous linear response, and centroids) are determined via path-integral Monte Carlo simulations in the canonical ensemble by utilizing the Aziz-Slaman and the SAPT2 interatomic potentials. Additional results obtained with the application of two closures for triplets in r space, the Kirkwood superposition approximation and the Jackson-Feenberg convolution, are also reported. Besides, an analysis of the nonsuitability of quantum hard spheres for describing this system is included. The pair structures in k space are fixed via Ornstein-Zernike schemes appropriate for dealing with quantum diffraction effects in fluids. The effect on the quality of the computed isothermal compressibilities brought about by increasing the sample size in the simulations and by the subsequent application of a grand ensemble correction to the asymptotic behavior of the canonical pair radial correlation functions is also investigated. Furthermore, it is demonstrated analytically that the methods of classical statistical mechanics for dealing with the higher-order direct correlation functions remain fully valid for studying the higher-order correlations of path-integral centroids. By taking advantage of this result, the triplet structure factors for the centroid (also for the instantaneous) correlations are computed by following a number of distinct closures and methods that involve triplet direct correlation functions. The latter computations are intended to explore an alternative scheme to the very expensive fixing of triplet structure factors through direct path integral simulations, an alternative which is expected to yield the main features of these triplet quantities for this gas. Comparison with experiment is made wherever possible, and the results presented allow one to explain the substantial structural features existing in gaseous helium-3.

On static triplet structures in fluids with quantum behavior

“…6 Although the study of triplets has received a great deal of attention from the classical point of view, there is a dearth of information on the quantum fluid side of this topic. [7][8][9] Homogeneous and isotropic fluids, monatomic or describable by a monatomic model, will be considered in this article.…”

“…13 These c n functions together with their associated Ornstein-Zernike (OZn) equations are instrumental in defining and computing the fluid responses in the Fourier k-space [e.g., the structure factors S (2) (k) and S (3) (k 1 ,k 2 )]. 8,14 a) Email: msese@ccia.uned.es Furthermore, triplet structures in general are needed to understand a number of condensed matter problems. Throughout the years one finds, at least, the following three main groups of applications.…”

“…However, this use is not free from uncertainties. The quality of a given closure has then to be assessed by consistency tests [7][8][9]38 or by comparison with direct computer simulation results (MC = Monte Carlo, MD = molecular dynamics). 7,27,32,39,40 The point now is to consider the current use of MC/MD as the most powerful alternatives to triplet closures.…”

“…44 [The usefulness of c 2 (r) even extends to the computation of S (3) (k 1 ,k 2 ).] 8,9,27 All the aspects of this difficult question turn out to be of the utmost importance if the interest is focused on quantum fluids.…”

“…Apart from a number of studies focused only on the instantaneous structures and related to the connections between the triplet g ET 3 (r,s,u) and the density/pressure derivatives of the pair g ET 2 (r), [17][18][19][20] or to angular order parameters, 51 this author is not aware of other recent studies on quantum triplets than his own. [7][8][9] These latter applications were performed over a decade ago and combined PIMC simulations with the use of closures in the r and the k spaces to study quantum hard-sphere fluids 7,9 and gaseous helium-3 (T = 5.23 K). 8 The aim of this article is to resume the research on quantum triplet structures by analyzing some representative issues related to fluids in which quantum exchange can be neglected.…”